$J$ $K$ $L$ If: $ JK = 6x + 9$, $ KL = 7x + 9$, and $ JL = 122$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 9} + {7x + 9} = {122}$ Combine like terms: $ 13x + 18 = {122}$ Subtract $18$ from both sides: $ 13x = 104$ Divide both sides by $13$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $KL$ $ KL = 7({8}) + 9$ Simplify: $ {KL = 56 + 9}$ Simplify to find ${KL}$ : $ {KL = 65}$